1. Technical Field
The embodiments discussed herein relate to an optical information transmission technology, such as an optical multilevel signal pre-equalization circuit suitable for transmission and reception of an optical multilevel signal via an optical fiber, an optical multilevel signal pre-equalization transmitter, and a polarization multiplexed pre-equalization transmitter.
2. Related Art
The amount of information that can be transmitted by a single optical fiber (transmission capacity) has been increased to a limit by increasing the number of wavelength channels or the optical signal modulation speed, with the wavelength bandwidth of an optical fiber amplifier having been nearly exhausted. If the transmission capacity of the optical fiber is to be further increased, it is necessary to devise an improved signal modulation system and enable a number of optical signals to be packed in a limited frequency-range, to thereby increase the frequency-range utilization efficiency. For this purpose, utilization of optical multilevel modulation has been considered, and a number of studies have been reported. For example, QPSK (Quadrature Phase Shift Keying) involving four-level phase modulation is reported in R. A. Griffin, et al., “10 Gb/s Optical Differential Quadrature Phase Shift Key (DQPSK) Transmission using GaAs/AlGaAs Integration,” OFC2002, paper PD-FD6, 2002 (hereafter referred to as “Non-patent Document 1”). Long-distance transmission of a 16QAM signal using optical delay detection, which is a type of direct detection, is reported in N. Kikuchi and S. Sasaki, “Highly-sensitive Optical Multilevel Transmission of arbitrary QAM (Quadrature-Amplitude Modulation) Signals with Direct Detection,” J. of Lightwave Technology, Vol. 28, No. 1, 2010, pp. 123-130 (hereafter referred to as “Non-patent Document 2”). A 16 QAM signal coherent reception system combining polarization multiplexing is reported in P. J. Winzer, “Spectrally Efficient Long-Haul Optical Networking Using 112-Gb/s Polarization-Multiplexed 16-QAM,” Journal of Lightwave Technology, Vol. 28, No. 4, Feb. 15, 2010, pp. 547-556 (hereafter referred to as “Non-patent Document 3”). A system such that a sixteen-level optical multilevel signal is coherently received and then subjected to digital delay detection in a receiver for reception is reported in N. Kikuchi, “Phase-Noise Tolerant Coherent Polarization-Multiplexed 16QAM Transmission with Digital Delay-Detection,” Proceeding of ECOC 2011, Geneva, Switzerland, September 2011, Tu.3.A.5 (hereafter referred to as “Non-patent Document 4”).
FIG. 1 illustrates a complex phase plane (or a complex plane, a phaser plane, or an IQ plane) used for optical transmission, and signal constellations according to various known modulation systems. In FIG. 1, the signal points of the various optical multilevel signals (complex notation of optical field at decision timing) are plotted on the complex phase plane. FIG. 1A illustrates a signal point on the IQ plane. Each signal point can be indicated by complex Cartesian coordinates (IQ-coordinate) or the polar coordinates expressed by the amplitude r(n) and the phase φ(n) as illustrated. FIG. 1B illustrates quarternary phase shift keying (QPSK) in which two bits of information (00, 01, 11, 10) are transmitted with one symbol by using four values (0, π/2, π, −π/2) as the phase angle φ(n). FIG. 1C illustrates sixteen-level quadrature amplitude modulation (16QAM) which is widely used for wireless applications. In 16QAM, the signal points are arranged in a lattice, and 4-bits of information can be transmitted with one symbol. FIG. 1D illustrates a signal constellation for a 16QAM signal in which a phase pre-integration process, which is a transmitting side signal processing for cancelling the effect of delay detection, is performed by a system described in the aforementioned Non-patent Documents 2 and 4.
Optical delay detection or delay detection in an electric signal stage is a process for detecting a phase difference by causing interference between two chronologically successive symbols, in which the phase component of an output signal from a delay detector represents a phase difference Δφ between the two chronologically successive symbols. Thus, when a multilevel signal such as the 16QAM signal is used, the signal outputted from a receiving side delay detector has a signal constellation with inter-symbol interference which greatly differs from the original multilevel signal. Further, the amplitude component after delay detection represents the product of the amplitudes of the two chronologically successive symbols.
In order to prevent the development of such inter-symbol interference, Non-patent Document 2 introduces a phase pre-integration process. This is a process for integrating the phase of an optical signal on the transmitting side in advance on a symbol by symbol basis. The process involves substituting the phase of a signal with Σφ(n) without changing the signal amplitude r(n), φ(n) being the phase of each symbol.
The signal constellation for the 16QAM signal after the phase pre-integration process greatly differs from the original signal constellation, as illustrated in FIG. 1D. However, the phase pre-integration (phase adding process) and the delay detection (phase differential) process in the receiver cancel each other such that the phase component of the signal outputted from the delay detector becomes identical to the phase component of the original 16QAM signal. Thus, by combining the phase component and a separately detected amplitude component r(n) in the receiver, the signal constellation of the original 16QAM signal illustrated in FIG. 1C can be reproduced. Accordingly, by using the phase pre-integration process on the transmitting side, the multilevel signal of an arbitrary signal constellation can be utilized even when an optical receiver that uses optical delay detection or delay detection in an electric signal stage is used.
Meanwhile, in ultrahigh-speed optical fiber transmission, phenomena related to the optical fiber or parts used, such as chromatic dispersion, polarization mode dispersion, and bandwidth limitation, pose a significant limitation factor against an increase in transmission speed or transmission distance. Chromatic dispersion (CD) is a phenomenon in which light of different wavelengths is transmitted at different speeds in an optical fiber. The optical spectrum of an optical signal that is modulated at high speed contains different wavelength components, and these components arrive at the receiving end at different times due to the influence of dispersion. As a result, the optical waveform after transmission is known to cause large waveform distortion.
In order to avoid the influence of dispersion, a technology referred to as “chromatic dispersion compensation” (which may be hereafter simply referred to as “dispersion compensation”) is being considered. According to chromatic dispersion compensation, which is a technique for preventing optical waveform distortion, an optical device with inverse chromatic dispersion characteristics with respect to the optical fiber used in the transmission path is installed in the optical transmitter or the optical receiver so that the chromatic dispersion characteristics of the optical fiber can be cancelled.
Conventionally, approaches that have been considered have involved a dispersion compensation fiber with chromatic dispersion of the opposite sign from the transmission path, an optical interferometer, an optical circuit, an optical fiber grating, and the like. These approaches, however, require an extra cost for the optical device, and the amount of chromatic dispersion or the amount of variation thereof that can be obtained by the optical device is limited. For these reasons, the application of digital signal processing has been considered in recent years.
Optical pre-equalization (pre-distortion) transmission is a system for implementing such optical field equalization by an electric signal process on the transmitting side. According to the system, an optical field waveform such that an inverse function of chromatic dispersion is applied to the field of an optical signal in advance in the transmitter is generated, and the optical field waveform is transmitted in the optical fiber so as to cancel the influence of chromatic dispersion of the optical fiber itself. While the basic concept of the pre-equalization system has been around for several decades, a digital pre-equalization optical transmitter for implementing pre-equalization by high-speed digital signal processing has been proposed in recent years. The details of the technology are discussed in Killey, R., “Dispersion and nonlinearity compensation using electronic predistortion techniques,” Optical Fibre Communications and Electronic Signal Processing, 2005, The IEE Seminar on (Ref. No. 2005-11310) (hereafter referred to as “Non-patent Document 5”), for example. The pre-equalization signal processing discussed in the present specification is a rather a broad term, including the processes of spectral narrowing, which is linear filtering required on the transmitting side for optical multilevel transmission, and interpolation.
FIG. 2 illustrates a basic configuration of a conventional pre-equalization optical multilevel transmitter that pre-equalizes the influence of chromatic dispersion. In a conventional optical multilevel transmitter signal processing circuit 100, an input information signal 101 is inputted to a multilevel encoder 102 and converted into a one-sample/symbol multilevel signal string 103 digitally represented on a quadrature complex plane, as in the 16QAM signal (FIG. 1C). Then, a doubling interpolation circuit 104 converts the multilevel signal string 103 into a 2 samples/symbol multilevel signal string 105 by an over-sampling process. The multilevel signal string 105 is inputted to a pre-equalization circuit 106 that pre-equalizes the influence of chromatic dispersion. The pre-equalization circuit 106 superposes an inverse function of the chromatic dispersion characteristics of the transmission path onto the multilevel signal string 105 through a digital pre-equalization process. The real part and the imaginary part of the multilevel signal 107 after pre-equalization are respectively inputted to linear response compensation circuits 108-1 and 108-2 and nonlinear response compensation circuits 109-1 and 109-2. The linear response compensation circuits 108-1 and 108-2 and the nonlinear response compensation circuits 109-1 and 109-2 perform digital signal processing for providing inverse compensation for linear or nonlinear response degradation of a subsequent driver amplifier or optical modulator. The real part and the imaginary part of a digital multilevel signal generated by the signal processing are inputted to DA converters 110-1 and 110-2, respectively, and are thereby converted into high-speed analog modulation signals 111-1 and 111-2, respectively. The analog modulation signals 111-1 and 111-2 are amplified by driver amplifiers 112-1 and 112-2 to desired amplitudes and then inputted to two modulation input terminals (I, Q) of an IQ optical (field) modulator 115. The IQ optical (field) modulator 115 converts CW (continuous wave) laser light 114 outputted from a laser source 113 into an optical multilevel signal 117 that is pre-equalized for chromatic dispersion, and outputs the optical multilevel signal 117 via an output optical fiber 116.
FIG. 3 illustrates a conventional configuration of a pre-equalization optical multilevel transmitter using a phase pre-integration process. The transmitter side of the system transmits an optical multilevel signal while performing a phase pre-integration process. The receiver side of the system subjects the optical multilevel signal to optical delay detection or coherent detection, and then performs delay detection by digital operation so as to alleviate various degradations associated with optical multilevel transmission. The details of the present system are discussed in Non-patent Documents 2 and 4.
The phase pre-integration process is an operational process that cumulatively adds the phase component (angle) of a multilevel signal on a symbol by symbol basis. However, when the phase pre-integration process is applied to a two-dimensional multilevel signal, such as the 16QAM signal, as is, complex operational processes are required, such as (1) a process for converting the signal point positions expressed by Cartesian coordinates to polar coordinates; (2) a process for adding extracted phase information at high accuracy of 8 to 12 bits, for example; (3) a process for conversion to Cartesian coordinates by re-combing the added signal with amplitude. These processes may be resolved by an operational process using a middle code described in WO 2010/061784 A1 (hereafter referred to as “Patent Document 1”). The phase pre-integration process of FIG. 3 will be described in accordance with a configuration disclosed in Patent Document 1.
FIG. 3A illustrates an internal configuration of a signal processing circuit 120 of the conventional phase pre-integration optical multilevel transmitter. In the case of the signal processing circuit 120, an information signal 101 is inputted to an encoder 121 that uses a middle polar coordinate code, by which the information signal 101 is converted into a polar coordinate multilevel middle code (amplitude N states, phase M states) 122. The polar coordinate multilevel middle code 122 is inputted to a phase pre-integration circuit 123. The phase pre-integration circuit 123 performs a pre-integration operation for sequentially cumulatively adding the middle code of the phase portion, re-combines the middle code with the middle code for the original amplitude portion, and then outputs a middle code (amplitude N states, phase M states) 124 after phase pre-integration. The middle code after phase pre-integration is subjected to Cartesian coordinate conversion by a Cartesian coordinate conversion circuit 125, thereby producing a multilevel signal 126 after phase pre-integration. The subsequent configuration of the transmitter is the same as depicted in FIG. 2, and an optical multilevel signal 127 that has been subjected to phase pre-integration and chromatic dispersion pre-equalization is obtained via the output optical fiber 116.
A first reason for adopting the configuration using the middle code is so that the polar coordinate conversion required for the phase pre-integration process can be omitted by encoding the multilevel signal in polar coordinates from the beginning. A second reason is in order to decrease the amount of subsequent operation by the phase pre-integration circuit 123 or the Cartesian coordinate conversion circuit 125 by significantly limiting the number of states of the multilevel signal (the number of states of amplitude N, the number of states of phase M; N and M being integers on the order of 4 to 32, for example).
FIG. 3B illustrates a conventional configuration of the phase pre-integration circuit 123, in which the inputted polar coordinate multilevel middle code 122 is separated into an amplitude middle code 130 with the number of states N and a phase information signal 131 with the number of states M. The amplitude middle code 130 is delayed by a delay circuit 133-1. The phase information signal 131 is inputted to an integration circuit 132. An adder circuit 136 of the integration circuit 132 adds an inputted phase information signal φi and a phase integrated value Σφi−1 up to one symbol previously, and outputs the result as a phase information signal 134 after pre-integration (Σφi).
The number of states of the phase information signal is M. Thus, the adder circuit 136 can perform the addition by “modulo-M”, so that the circuit size required for the adding can be decreased. To the subsequent Cartesian coordinate conversion circuit 125, a multilevel signal with the number of amplitude states N and the number of phase states M is inputted. The Cartesian coordinate conversion circuit 125 may be implemented by using a look-up table (LUT).
FIG. 4A illustrates a 16QAM signal discussed in Patent Document 1 and an example of the middle code thereof. In the present example, the amplitude has three levels, and the phase has sixteen levels. Thus, the amplitude of the middle code is expressed by 2 bits, with 00, 01, and 10 allocated to a minimum value r1, a middle value r2, and a maximum value r3, respectively. The number of states of the phase of the middle code M=16, and the phase of the middle code is expressed by 16 values of 4-bits from 0000 to 1111.
FIG. 4B illustrates a signal constellation after phase pre-integration. In FIG. 4B, the phase state of the 16QAM signal is limited to positions corresponding to integer multiples of 2π/16. The number of phase states before and after phase pre-integration is both M=16. Thus, the middle code with the amplitude of three levels and the phase of sixteen levels can be commonly used before and after phase pre-integration.
FIG. 5 illustrates a configuration in which the conventional chromatic dispersion pre-equalization circuit 106 is implemented by a complex digital FIR (Finite Impulse Response) filter. The complex digital FIR filter 140 is a circuit in which complex delay circuits 141, complex tap multipliers 142, and adders 143 are arranged in ladder form. The response characteristics of the complex tap multipliers 142 are set at d−1 (t), which is the impulse response of an inverse function D−1 (f) of the chromatic dispersion of transmission path. The complex tap multipliers 142 implements a pre-equalization function that convolves the impulse response d−1 (t) with the two-samples/symbol multilevel signal string 105 that has been inputted.
However, this configuration requires one complex multiplier per tap (which is equivalent to four real number multipliers). Further, in this configuration, when the transmission distance is long and the influence of chromatic dispersion is increased, it becomes necessary to take longer impulse response d(t), resulting in the problem that the amount of operation (i.e., circuit size) drastically increases in proportion to the amount of chromatic dispersion.
For example, when the symbol speed of the optical multilevel signal is 28 G symbols/s, the sampling speed of digital signal processing is twice that, i.e., 56 G samples/s, and the transmission distance of the optical fiber is 100 km (with the amount of chromatic dispersion of 1700 ps/nm for normal dispersion fiber), the optical pulse energy amount due to chromatic dispersion in a signal bandwidth of ±56 GHz is about 761 ps=8 symbols. The required number of taps for the FIR filter in this case is twice as many, i.e., 16 taps. Although the number of taps may appear small, the operation speed of an IC circuit for performing these operational processes is on the order of no more than several 100 MHz. Thus, when the FIR filter is configured from 200 or so parallel operations, the number of required real number multipliers will be 16×4×200=12800, thus requiring a very large-sized complex operation circuit.
As a method for alleviating the problem of an increase in circuit size, the pre-equalization circuit for chromatic dispersion may be configured from look-up tables, as illustrated in FIG. 2 of Non-patent Document 5. In the pre-equalization circuit, an ideal optical multilevel signal prior to transmission can be used as an input signal. Further, by utilizing the look-up tables, circuit size can be greatly decreased because the number of states of the field signal that is inputted can be greatly decreased. Namely, assuming a general complex field input, the input field signal would have a number of states on the order of 16 bits of 8 bits for real part and 8 bits for imaginary part (corresponding to 65536 states). However, when the ideal binary field signal prior to transmission is inputted, for example, one bit for mark and space would suffice, so that the circuit size can be decreased to 1/65536. Accordingly, the pre-equalization circuit can be configured by using a memory circuit of a relatively small size.
FIG. 6A illustrates a configuration of such a conventional pre-equalization transmitter. The pre-equalization transmitter includes an optical multilevel transmitter signal processing circuit 150 that uses a look-up table type pre-equalization circuit for pre-equalization of the chromatic dispersion of a binary or multilevel optical signal for transmission. When the information signal 101 to be transmitted is a bit string di, the input signal is inputted to a buffer circuit (FIFO: First In First Out) 151 in which di is extracted from a data string d(i−n+1) for n symbols and inputted to the look-up table type pre-equalization circuit 152.
The look-up table type pre-equalization circuit 152 is provided with an over-sampling process and outputs two time sample points per symbol for two sets of interpolation samples of times 2i and 2i+1, for example, as a complex field signal (two sets of digital data for real part and imaginary part). The reason that the look-up table type pre-equalization circuit 152 can be used is that, when the time length of the digital complex FIR filter is n symbols (the number of taps is 2n when the over-sampling coefficient is two), the waveform of the output complex optical signal of the times 2i and 2i+1 is uniquely determined only by the input data for the n symbols immediately preceding the times. Namely, the same function as an FIR filter can be implemented by creating a look-up table with the output waveforms for the two times as values by using the data for the immediately preceding n symbols as addresses.
FIG. 6B illustrates a configuration of the look-up table type pre-equalization circuit 152 in a case where the input signal di is a binary signal. A data string di−n+1 to di for n bits that have been inputted is utilized as addresses for the n bits, and the real part and the imaginary part of data for timings 2i and 2i+1 are each stored as 8-bit data. In the present example, the size of the look-up table type pre-equalization circuit 152 is (2n×4) bytes. For example, when n=10, the circuit size of the look-up table type pre-equalization circuit 152 only needs to be on the order of as small as 128 bytes. Further, Non-patent Document 5 discusses a configuration such that the look-up table type pre-equalization circuit 152 includes the function of correcting a nonlinear response of the IQ optical (field) modulator 115 or a bandwidth response of a driver circuit.